Geometry - von Staudt's Point of View

K. Strambach

ISBN 10: 9027712832 / ISBN 13: 9789027712837

Published by Springer Netherlands, Springer Netherlands Mai 1981, 1981

About this Item

Neuware -Ever since F. Klein designed his 'Erlanger programm', geometries have been studied in close connection with their groups of automorphisms. It must be admitted that the presence of a large automorphismgroup does not always have strong implications for the incidence-th- retical behaviour of a geometry. For exampl~ O. H. Kegel and A. Schleiermacher [Geometriae Dedicata 2, 379 - 395 (1974)J constructed a projective plane with a transitive action of its collineation group on quadrangles, in which, nevertheless every four points generate a free subplane. However, there are several important special classes of geometries, in which strong implications are present. For instance, every finite projective plane with a doubly transitive collineation group is pappian (Theorem of Ostrom-Wagner), and every compact connected projective plane with a flag-transitive group of continuous collineations is a Moufang plane (H. Salzmann, Pac. J. Math. ~, 217 - 234 (1975)]. Klein's point of view has been very useful for numerous incidence structures and has established an intimate connection between group theory and geometry vii P. Plaumann and K. Strambach (eds. ), Geometry - von Staudt's Point of View, vii-xi. Copyright 1981 by D. Reidel Publishing Company. viii PREFACE 1. 1:1ich is a guidepost for every modern t:reat:ment of geometry. A few decades earlier than Klein's proposal, K. G. Ch. von Staudt stated a theorem which indicates a different point of view and is nowadays sometimes called the 'Fundamental Theorem of Projective Geometry'.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 448 pp. Englisch.

Seller Inventory # 9789027712837

Bibliographic Details

• Title: Geometry - von Staudt's Point of View
• Publisher: Springer Netherlands, Springer Netherlands Mai 1981
• Publication Date: 1981
• Language: English
• ISBN 10: 9027712832
• ISBN 13: 9789027712837
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 29D millimeters 241 millimeters width by 160 millimeters height by 29 millimeters depth
• Weight: 834 grams

About this title

Synopsis

Ever since F. Klein designed his "Erlanger programm", geometries have been studied in close connection with their groups of automorphisms. It must be admitted that the presence of a large automorphismgroup does not always have strong implications for the incidence-th- retical behaviour of a geometry. For exampl O. H. Kegel and A. Schleiermacher [Geometriae Dedicata 2, 379 - 395 (1974)J constructed a projective plane with a transitive action of its collineation group on quadrangles, in which, nevertheless every four points generate a free subplane. However, there are several important special classes of geometries, in which strong implications are present. For instance, every finite projective plane with a doubly transitive collineation group is pappian (Theorem of Ostrom-Wagner), and every compact connected projective plane with a flag-transitive group of continuous collineations is a Moufang plane (H. Salzmann, Pac. J. Math., 217 - 234 (1975)]. Klein's point of view has been very useful for numerous incidence structures and has established an intimate connection between group theory and geometry vii P. Plaumann and K. Strambach (eds. ), Geometry - von Staudt's Point of View, vii-xi. Copyright (c) 1981 by D. Reidel Publishing Company. viii PREFACE 1. 1:1ich is a guidepost for every modern t: reat: ment of geometry. A few decades earlier than Klein's proposal, K. G. Ch. von Staudt stated a theorem which indicates a different point of view and is nowadays sometimes called the "Fundamental Theorem of Projective Geometry".